Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive.\newlineb94b14b^{\frac{9}{4}} \cdot b^{\frac{1}{4}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______

Full solution

Q. Simplify. Assume all variables are positive.\newlineb94b14b^{\frac{9}{4}} \cdot b^{\frac{1}{4}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
  1. Identify Equation and Apply Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: \newlinebmn×bpq=bmn+pqb^{\frac{m}{n}} \times b^{\frac{p}{q}} = b^{\frac{m}{n} + \frac{p}{q}}
  2. Add Exponents: Add the exponents (94)(\frac{9}{4}) and (14)(\frac{1}{4}).94+14=9+14=104\frac{9}{4} + \frac{1}{4} = \frac{9 + 1}{4} = \frac{10}{4}
  3. Simplify Fraction: Simplify the fraction 104\frac{10}{4}. 104\frac{10}{4} can be simplified to 52\frac{5}{2} by dividing both the numerator and the denominator by 22.
  4. Write Final Answer: Write the final answer using the simplified exponent. b104b^{\frac{10}{4}} simplifies to b52b^{\frac{5}{2}}.

More problems from Simplify expressions involving rational exponents